Dmisteinbergite, CaAl 2 Si 2 O 8 , a Metastable Polymorph of Anorthite: Crystal-Structure and Raman Spectroscopic Study of the Holotype Specimen

: The crystal structure of dmisteinbergite has been determined using crystals from the type locality in Kopeisk city, Chelyabinsk area, Southern Urals, Russia. The mineral is trigonal, with the following structure: P 312, a = 5.1123(2), c = 14.7420(7) Å, V = 333.67(3) Å 3 , R 1 = 0.045, for 762 unique observed reﬂections. The most intense bands of the Raman spectra at 327s, 439s, 892s, and 912s cm − 1 correspond to di ﬀ erent types of tetrahedral stretching vibrations: Si–O, Al–O, O–Si–O, and O–Al–O. The weak bands at 487w, 503w, and 801w cm − 1 can be attributed to the valence and deformation modes of Si–O and Al–O bond vibrations in tetrahedra. The weak bands in the range of 70–200 cm − 1 can be attributed to Ca–O bond vibrations or lattice modes. The crystal structure of dmisteinbergite is based upon double layers of six-membered rings of corner-sharing AlO 4 and SiO 4 tetrahedra. The obtained model shows an ordering of Al and Si over four distinct crystallographic sites with tetrahedral coordination, which is evident from the average < T –O > bond lengths (T = Al, Si), equal to 1.666, 1.713, 1.611, and 1.748 Å for T1, T2, T3, and T4, respectively. One of the oxygen sites (O4) is split, suggesting the existence of two possible conformations of the [Al 2 Si 2 O 8 ] 2 − layers, with di ﬀ erent systems of ditrigonal distortions in the adjacent single layers. The observed disorder has a direct inﬂuence upon the geometry of the interlayer space and the coordination of the Ca2 site. Whereas the coordination of the Ca1 site is not inﬂuenced by the disorder and is trigonal antiprismatic (distorted octahedral), the coordination environment of the Ca2 site includes disordered O atoms is either trigonal prismatic or trigonal antiprismatic. The observed structural features suggest the possible existence of di ﬀ erent varieties of dmisteinbergite that may di ﬀ er in: (i) degree of disorder of the Al / Si tetrahedral sites, with completely disordered structure having the P 6 3 / mcm symmetry; (ii) degree of disorder of the O sites, which may have a direct inﬂuence on the coordination features of the Ca 2 + cations; (iii) polytypic variations (di ﬀ erent stacking sequences and layer shifts). The formation of dmisteinbergite is usually associated with metastable crystallization in both natural and synthetic systems, indicating the kinetic nature of this phase. Information-based complexity calculations indicate that the crystal structures of metastable CaAl are structurally and topologically simpler than that of their stable counterpart, anorthite, which is in good agreement with Goldsmith’s simplexity principle and similar previous observations.


Single-crystal X-ray diffraction
Single-crystal X-ray diffraction study of dmisteinbergite was performed at the X-ray Diffraction Methods Resource Center of St. Petersburg State University using a Bruker Kappa APEX II DUO diffractometer operated at 45 kV and 0.6 mA (microfocus tube) and equipped with a CCD area detector. The study was done by means of monochromatic MoKα X-radiation (λ = 0.71073 Å), frame widths of 0.5° in ω, and with 10 s counting time for each frame. The intensity data were reduced and corrected for Lorentz, polarization, and background effects using the Bruker software APEX2 [43]. A semiempirical absorption correction based upon the intensities of equivalent reflections was applied using SADABS [44]. The unit cell parameters were refined by least square techniques using 2898 reflections. The structure was solved and refined in the space group P312 to R1 = 0.045 (wR2 = 0.136) for 703 unique observed reflections with I ≥ 2σ(I) using the ShelX program package [45] within the Olex2 shell [46]. The merohedral twinning model was introduced into the refinement at the later stage by applying the matrix [100/010/00-1] with (001) as a twin plane. The resulting ratio of the two twin components was 0.51:0.49. During the refinement, a relatively large electron density peak was observed near the O4 atom, indicating splitting of this position into two sites. The splitting was modeled by introducing an additional O4A site with the O4-O4A distance of 1.13(1) Å. The refinement of the occupancies of the split sites (constrained to be equal to 1) resulted in the site occupation factors of 0.60(1) and 0.40 (1) for O4 and O4A, respectively. We note that no disorder of O sites was reported in the previous crystallographic works on dmisteinbergite [30,36]. Crystal data, data collection information, and refinement details are given in Table 1. Atom coordinates, site occupancies, and displacement parameters are listed in Table 2 and Table S1, whereas Table 3 contains selected interatomic distances. Table 4 provides the results of bond valence analysis with the bond valence parameters taken from a previous study [47].

Single-Crystal X-ray Diffraction
Single-crystal X-ray diffraction study of dmisteinbergite was performed at the X-ray Diffraction Methods Resource Center of St. Petersburg State University using a Bruker Kappa APEX II DUO diffractometer operated at 45 kV and 0.6 mA (microfocus tube) and equipped with a CCD area detector. The study was done by means of monochromatic MoKα X-radiation (λ = 0.71073 Å), frame widths of 0.5 • in ω, and with 10 s counting time for each frame. The intensity data were reduced and corrected for Lorentz, polarization, and background effects using the Bruker software APEX2 [43]. A semiempirical absorption correction based upon the intensities of equivalent reflections was applied using SADABS [44]. The unit cell parameters were refined by least square techniques using 2898 reflections. The structure was solved and refined in the space group P312 to R 1 = 0.045 (wR 2 = 0.136) for 703 unique observed reflections with I ≥ 2σ(I) using the ShelX program package [45] within the Olex2 shell [46]. The merohedral twinning model was introduced into the refinement at the later stage by applying the matrix [100/010/00-1] with (001) as a twin plane. The resulting ratio of the two twin components was 0.51:0.49. During the refinement, a relatively large electron density peak was observed near the O4 atom, indicating splitting of this position into two sites. The splitting was modeled by introducing an additional O4A site with the O4-O4A distance of 1.13(1) Å. The refinement of the occupancies of the split sites (constrained to be equal to 1) resulted in the site occupation factors of 0.60(1) and 0.40(1) for O4 and O4A, respectively. We note that no disorder of O sites was reported in the previous crystallographic works on dmisteinbergite [30,36]. Crystal data, data collection information, and refinement details are given in Table 1. Atom coordinates, site occupancies, and displacement parameters are listed in Table 2 and Table S1, whereas Table 3 contains selected interatomic distances. Table 4 provides the results of bond valence analysis with the bond valence parameters taken from a previous study [47].

Raman Spectroscopy
Raman spectra of dmisteinbergite ( Figure 2) were collected from the surfaces of hexagonal transparent plates at the Geomodel Resource Center of St. Petersburg State University using a Horiba Jobin-Yvon LabRam HR 800 system at room temperature using a 514 nm laser. The Raman spectra were recorded up to 1200 cm −1 . No peaks were observed in the region of 1200-4000 cm −1 .

Raman Spectroscopy
Raman spectra of dmisteinbergite ( Figure 2) were collected from the surfaces of hexagonal transparent plates at the Geomodel Resource Center of St. Petersburg State University using a Horiba Jobin-Yvon LabRam HR 800 system at room temperature using a 514 nm laser. The Raman spectra were recorded up to 1200 cm −1 . No peaks were observed in the region of 1200-4000 cm −1 .

Raman Spectroscopy
The Raman spectrum of dmisteinbergite from the burned dumps of the Chelyabinsk coal basin is very similar to the published spectra of dmisteinbergite from the RRUFF Raman database [48] ( Figure 2). The data were compared with the material from the deposit near Katashina village, Gunma Prefecture, Japan (RRUFF identification code R130087), and with the material from the meteorite NWA 2086 (RRUFF identification code R130085, museum of the University of Szeged, Hungary) [9].
At least six of the strongest bands in the region of 200-1200 cm −1 (327, 439, 503, 801, 892, and 912 cm −1 ) match well in those dmisteinbergite spectra, and four bands (327, 439, 801, 912 cm −1 ) match with dmisteinbergite from the Gole Larghe fault (Italian Alps) [18]. Interpretation of the bands present in the Raman spectra of dmisteinbergite is given in Table 5. The most intense bands at 327s, 439s, 892s, and 912s cm −1 correspond to the symmetric modes of stretching and bending vibrations in tetrehedra: The weak bands at 487w, 503w, and 801w cm −1 were attributed

Raman Spectroscopy
The Raman spectrum of dmisteinbergite from the burned dumps of the Chelyabinsk coal basin is very similar to the published spectra of dmisteinbergite from the RRUFF Raman database [48] ( Figure 2). The data were compared with the material from the deposit near Katashina village, Gunma Prefecture, Japan (RRUFF identification code R130087), and with the material from the meteorite NWA 2086 (RRUFF identification code R130085, museum of the University of Szeged, Hungary) [9].
At least six of the strongest bands in the region of 200-1200 cm −1 (327, 439, 503, 801, 892, and 912 cm −1 ) match well in those dmisteinbergite spectra, and four bands (327, 439, 801, 912 cm −1 ) Minerals 2019, 9, 570 6 of 12 match with dmisteinbergite from the Gole Larghe fault (Italian Alps) [18]. Interpretation of the bands present in the Raman spectra of dmisteinbergite is given in Table 5. The most intense bands at 327s, 439s, 892s, and 912s cm −1 correspond to the symmetric modes of stretching and bending vibrations in tetrehedra: Si-O, Al-O, O-Si-O, and O-Al-O [49]. The weak bands at 487w, 503w, and 801w cm −1 were attributed to the asymmetric stretching and deformation modes of Si-O and Al-O bond vibrations in tetrahedra. The weak bands in the range of 70-200 cm −1 can be attributed to Ca-O bond vibrations or lattice modes. The presence of additional bands in the spectra of sample NWA 2086 (1002w, 1122w, and 1194w cm −1 ) and dmisteinbergite from the Chelyabinsk coal basin [40] (484s, 650s, and 935s cm −1 ) are most likely due to the nano-sized (<1 µm) inclusions of quartz and anorthite.

Crystal Structure
The crystal structure of dmisteinbergite is based upon double layers of six-membered rings of corner-sharing AlO 4 and SiO 4 tetrahedra (Figure 3a). The high-symmetry P6 3 /mcm structure model for dmisteinbergite ("hexagonal anorthite"), which was previously reported [30,36], implies completely disordered distribution of Si and Al over one crystallographically independent tetrahedral site. In contrast, our model obtained in the space group P312 shows at least partial order of Al and Si over four distinct crystallographic sites with tetrahedral coordination. The existence of order is evident from the average <T-O> bond lengths (T = Al, Si), which are equal to 1.666, 1.713, 1.611, and 1.748 Å for T1, T2, T3, and T4, respectively. Therefore, T1 and T3 sites are predominantly occupied by Si, whereas the T2 and T4 sites are predominantly occupied by Al. The P6 3 /mcm structure model was first determined by Takeuchi and Donnay in 1959 [30] and refined to the essentially high crystallographic agreement index R 1 = 13.8%. Dimitrijević et al. [36] refined the structure from the powder diffraction data using the Rietveld method and obtained the final agreement factors R P = 8.99%, R wp = 11.87%, and R B = 4.31%. The refinement was done using the model of Takeuchi and Donnay [30] from the mixture of dmisteinbergite and anorthite with the ratio 30:70% obtained by annealing Ca-LTA zeolite over 900 • C. The authors pointed out that the anorthite phase was of pure crystallinity, which increased the number of additional diffraction peaks and created considerable problems when refining the profile parameters. Under further annealing, the mixture transformed into pure anorthite, indicating the metastable character of dmisteinbergite. Considering the abovementioned problems in the previous studies, we believe that the P312 model is probably more correct, considering its general agreement with the basic crystal chemical principles, such as ordered arrangement of Al and Si atoms over tetrahedral sites.
The suggested splitting of the O4 site in dmisteinbergite implies the existence of two possible conformations of the [Al 2 Si 2 O 8 ] 2− layers. The nature of the conformation can be described by the in-plane rotation of tetrahedra around the c axis. This phenomenon is well-known and has been studied in detail for minerals of the mica group [50,51]. The ideal tetrahedral layer formed by a six-membered ring has a hexagonal symmetry, with basal O atoms forming perfect hexagonal rings. The layers are actually distorted according to a ditrigonal rotation, which is defined as a rotation of tetrahedra around the axis perpendicular to the plane of the layer (Figure 4). The degree of the distortion is specified by the tetrahedral rotation angle α, which in dmisteinbergite is 22.1 • . The directions of ditrigonal rotation in two adjacent layers comprising a double layer may be either identical (++ or −−) or opposite (+− or −+). The former case is realized when the O4 site is occupied, and therefore, the layers have the configuration shown in Figure 3b. The latter case is realized when the O4A site is occupied and the O4 site is vacant (Figure 3c). 8.99%, Rwp = 11.87%, and RB = 4.31%. The refinement was done using the model of Takeuchi and Donnay [30] from the mixture of dmisteinbergite and anorthite with the ratio 30:70% obtained by annealing Ca-LTA zeolite over 900 °C. The authors pointed out that the anorthite phase was of pure crystallinity, which increased the number of additional diffraction peaks and created considerable problems when refining the profile parameters. Under further annealing, the mixture transformed into pure anorthite, indicating the metastable character of dmisteinbergite. Considering the abovementioned problems in the previous studies, we believe that the P312 model is probably more correct, considering its general agreement with the basic crystal chemical principles, such as ordered arrangement of Al and Si atoms over tetrahedral sites.  The suggested splitting of the O4 site in dmisteinbergite implies the existence of two possible conformations of the [Al2Si2O8] 2− layers. The nature of the conformation can be described by the inplane rotation of tetrahedra around the c axis. This phenomenon is well-known and has been studied in detail for minerals of the mica group [50,51]. The ideal tetrahedral layer formed by a six-membered ring has a hexagonal symmetry, with basal O atoms forming perfect hexagonal rings. The layers are actually distorted according to a ditrigonal rotation, which is defined as a rotation of tetrahedra around the axis perpendicular to the plane of the layer (Figure 4). The degree of the distortion is specified by the tetrahedral rotation angle α, which in dmisteinbergite is 22.1°. The directions of ditrigonal rotation in two adjacent layers comprising a double layer may be either identical (++ or −−) or opposite (+− or −+). The former case is realized when the O4 site is occupied, and therefore, the layers have the configuration shown in Figure 3b. The latter case is realized when the O4A site is occupied and the O4 site is vacant (Figure 3c).
The disorder of the O4 site also has a direct influence on the geometry of the interlayer space and coordination of the Ca atoms. There are two independent Ca sites in the crystal structure of dmisteinbergite. Coordination of the Ca1 site is not influenced by the disorder and is trigonal antiprismatic (distorted octahedral) (Figure 5b). In contrast, the coordination environment of the Ca2 site includes O4 and O4A atoms, and therefore, depends on the occupancies of the disordered O sites. If one of the two sites is occupied in both upper and lower tetrahedral layers (e.g., O4-O4 and O4A-O4a), the coordination is trigonal antiprismatic (Figure 5b; the A-type interlayer). However, if the occupancies of the sites are different (e.g., if the O4 site is occupied in the upper layer and the O4A site is occupied in the lower layer), the coordination becomes trigonal prismatic ( Figure 5a; the B-type interlayer). Ferraris and Ivaldi [51] noted that for mica-group minerals, polytypes with the A-type interlayer are more stable than those with the B-type interlayer. It is also noteworthy that the value of the ditrigonal rotation angle α (22.1°) is in good agreement with the values reported for Ca-bearing micas that have Ca 2+ cations as interlayer species. For instance, in the crystal structure of clintonite, Ca(Mg,Al)3(Al3SiO10)(OH)2, the α value is in the range of 23.1-24.9° [52]. The typical value of α for the rock-forming micas is in the range of 7-9° [50].  The disorder of the O4 site also has a direct influence on the geometry of the interlayer space and coordination of the Ca atoms. There are two independent Ca sites in the crystal structure of dmisteinbergite. Coordination of the Ca1 site is not influenced by the disorder and is trigonal antiprismatic (distorted octahedral) (Figure 5b). In contrast, the coordination environment of the Ca2 site includes O4 and O4A atoms, and therefore, depends on the occupancies of the disordered O sites. If one of the two sites is occupied in both upper and lower tetrahedral layers (e.g., O4-O4 and O4A-O4a), the coordination is trigonal antiprismatic (Figure 5b; the A-type interlayer). However, if the occupancies of the sites are different (e.g., if the O4 site is occupied in the upper layer and the O4A site is occupied in the lower layer), the coordination becomes trigonal prismatic (Figure 5a; the B-type interlayer). Ferraris and Ivaldi [51] noted that for mica-group minerals, polytypes with the A-type interlayer are more stable than those with the B-type interlayer. It is also noteworthy that the value of the ditrigonal rotation angle α (22.1 • ) is in good agreement with the values reported for Ca-bearing micas that have Ca 2+ cations as interlayer species. For instance, in the crystal structure of clintonite, Ca(Mg,Al) 3 (Al 3 SiO 10 )(OH) 2 , the α value is in the range of 23.1-24.9 • [52]. The typical value of α for the rock-forming micas is in the range of 7-9 • [50].

Discussion
The observed features of the crystal structure of dmisteinbergite from the type locality suggest the potential existence of different types of "hexagonal anorthite" that may differ in: (i) degree of disorder of the Al/Si tetrahedral sites, with completely disordered structure having the P63/mcm symmetry; (ii) degree of disorder of the O sites (particularly O4 site), which have a direct influence upon the coordination of the Ca 2+ cations (Ca2 site); (iii) polytypic variations (different stacking sequences and layer shifts). These features may explain, at least in part, the different symmetries reported for natural and synthetic dmisteinbergite [30,32,36,42]. It is interesting that the Raman spectra of dmisteinbergite crystals from different localities are slightly different, suggesting variable degrees of the Al/Si ordering by analogy with anorthite [53]. As was noted in a previous study [53], the peaks of symmetric bending vibrations of Si-O and Al-O bonds at 488 cm −1 for the most ordered anorthite species shifted to 485 cm −1 in shocked type anorthite and HT (high-temperature) anorthite. If this approach is used for the bands in the same range for dmisteinbergite spectra, then the sample from NWA 2086 meteorite should be more disordered dmisteinbergite (and sample from Katashina, Japan should be more ordered dmisteinbergite).
The formation of dmisteinbergite is usually associated with metastable crystallization in both natural [6,8,9,[18][19][20] and synthetic [32][33][34][35][54][55][56] systems, indicating the kinetic nature of this phase. In the burned coal dumps, dmisteinbergite crystallizes directly from the gaseous phases together with the other metastable anorthite polymorph, svyatoslavite. Goldsmith [21] suggested that metastable, kinetically stabilized phases are usually structurally simpler than their stable counterparts. The complexity of crystal structures can be estimated using the information-based approach developed in previous studies [22,57]. The calculations of the structural complexity parameters for different anorthite polymorphs were performed using the TOPOSPro software package [58] and the values are given in Table 6. It can be seen that the crystal structures of the metastable CaAl2Si2O8 polymorphs dmisteinbergite and svyatoslavite are much simpler than that of anorthite, in good agreement with Goldsmith's principle and similar previous observations [22][23][24][25][26][27][28]59,60].

Discussion
The observed features of the crystal structure of dmisteinbergite from the type locality suggest the potential existence of different types of "hexagonal anorthite" that may differ in: (i) degree of disorder of the Al/Si tetrahedral sites, with completely disordered structure having the P6 3 /mcm symmetry; (ii) degree of disorder of the O sites (particularly O4 site), which have a direct influence upon the coordination of the Ca 2+ cations (Ca2 site); (iii) polytypic variations (different stacking sequences and layer shifts). These features may explain, at least in part, the different symmetries reported for natural and synthetic dmisteinbergite [30,32,36,42]. It is interesting that the Raman spectra of dmisteinbergite crystals from different localities are slightly different, suggesting variable degrees of the Al/Si ordering by analogy with anorthite [53]. As was noted in a previous study [53], the peaks of symmetric bending vibrations of Si-O and Al-O bonds at 488 cm −1 for the most ordered anorthite species shifted to 485 cm −1 in shocked type anorthite and HT (high-temperature) anorthite. If this approach is used for the bands in the same range for dmisteinbergite spectra, then the sample from NWA 2086 meteorite should be more disordered dmisteinbergite (and sample from Katashina, Japan should be more ordered dmisteinbergite).
The formation of dmisteinbergite is usually associated with metastable crystallization in both natural [6,8,9,[18][19][20] and synthetic [32][33][34][35][54][55][56] systems, indicating the kinetic nature of this phase. In the burned coal dumps, dmisteinbergite crystallizes directly from the gaseous phases together with the other metastable anorthite polymorph, svyatoslavite. Goldsmith [21] suggested that metastable, kinetically stabilized phases are usually structurally simpler than their stable counterparts. The complexity of crystal structures can be estimated using the information-based approach developed in previous studies [22,57]. The calculations of the structural complexity parameters for different anorthite polymorphs were performed using the TOPOSPro software package [58] and the values are given in Table 6. It can be seen that the crystal structures of the metastable CaAl 2 Si 2 O 8 polymorphs dmisteinbergite and svyatoslavite are much simpler than that of anorthite, in good agreement with Goldsmith's principle and similar previous observations [22][23][24][25][26][27][28]59,60]. It is also of interest to evaluate the topological complexity of aluminosilicate tetrahedral units in anorthite, dmisteinbergite, and svyatoslavite. The topological complexity is defined as the information-based complexity of the atomic arrangement with the highest possible symmetry. According to Baerlocher et al. [61], the tetrahedral framework in svyatoslavite corresponds to the BCT zeolite framework type with the I4/mmm ideal space-group symmetry. The ideal symmetry of the double tetrahedral layer in dmisteinbergite is described by the subperiodic layer group p6/mmm. The ideal (topological) symmetry of the feldspar framework is C2/m [62]. The information-based topological complexity parameters for the aluminosilicate units are given in Table 6, considering calculations of zeolite frameworks reported in a previous study [63]. It is evident that topological complexities of the tetrahedral units in three CaAl 2 Si 2 O 8 polymorphs are in agreement with Goldsmith's principle as well-kinetically stable but thermodynamically metastable phases are topologically simpler than thermodynamically stable ones. It is sometimes inferred that the formation of particular metastable polymorphs in aluminosilicate systems is determined by the structure of the initial melt [4]. However, this argument is not valid in our case, as the structures of the two metastable CaAl 2 Si 2 O 8 polymorphs are topologically different. In addition, crystallization from the gaseous phase does not involve any reasonable melting state. Therefore, we suggest that metastable crystallization in feldspar systems is a configurational entropy-driven process, where complexity is a major driving force as a parameter closely associated with the configurational entropy of atomic arrangements [64].